# Stairway

Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.

Correct result:

x =  552.541 cm

#### Solution:

$a=\sqrt{ (20 \cdot \ 22)^{ 2 }+(20 \cdot \ 15)^{ 2 } }=20 \ \sqrt{ 709 } \ \text{cm} \doteq 532.5411 \ \text{cm} \ \\ x=2 \cdot \ 10 + a=2 \cdot \ 10 + 532.5411=552.541 \ \text{cm}$

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